A stone fell down and broke into 2 pieces whose weights are in ratio 3:4.The value of the stone varies with the square of its weight.If the loss in the value of the stone due to breakage is 9600 rupees,the value of the original stone is__________.
Let actual weight = W
and then its price = kW let k = 1 , where k is proportionality constant
Thus, price = W^2
now it get broke into ratio 3 : 4
let those pieces weigh 3x and 4x
3x+4x = W
Or 7x = W
Or x= W/7
so those pieces gonna weigh = , 3W/7and 4W/7
and therefore there prices would be = 9W^2/49 and 16W^2/49
total price = 9W^2/49 + 16W^2/49 = 25W^2/49
loss in actual price = W^2 - 25W^2/49 = 24W^2/49
But the given loss is RS 9600.
Then , 24w^2/ 49= Rs9600
Or, W^2 = Rs 19600 , where W^ 2 is actual price.
Hence , actual price is Rs 19600.